JP5248958B2 - Three-dimensional position designation device, three-dimensional position designation program, voxel modeling device, and voxel modeling program - Google Patents

Description

  The present invention relates to a three-dimensional position specifying device for specifying a three-dimensional position in a three-dimensional space, a three-dimensional position specifying method, a program for specifying a three-dimensional position, and voxel modeling for expressing a three-dimensional shape as a set of voxels. The present invention relates to a device, a voxel modeling method, and a voxel modeling program.

With the improvement of computing performance and graphic performance of computers, designs using 3D CAD (Computer Aided Design) and 3D CG (Computer Graphics) have become widespread. A three-dimensional GUI (Graphical User Interface) based on a three-dimensional CG that enables display and operation has also been proposed. Conventionally, as a technique for pointing to a desired point in a three-dimensional space expressed on a DFD (Depth-fused 3D) display device, the indication position 2 when pointing on the detection surface with the pen tip of the input pen is used. A method for pointing a desired point in the three-dimensional space based on the dimensional coordinates and the writing pressure, which is the pressure applied to the pen tip of the input pen, or the operation time of the input means provided in the input pen, or the input Proposed a method of changing the coordinate in the depth direction of the three-dimensional pointer displayed in the three-dimensional space represented on the DFD display device in accordance with the pen pressure or the duration of the instruction or the operation of the operation means provided in the input pen. (For example, refer to Patent Document 1).
WO2006 / 041097

  As described above, in order to handle three-dimensional coordinates and three-dimensional shapes in the three-dimensional space, in addition to the X-axis direction and the Y-axis direction in the two-dimensional space, absolute coordinates or relative coordinates in the Z-axis direction (depth direction) are set. It is necessary to specify. However, it is not easy to accurately specify the position in the depth direction on a two-dimensional space, that is, a two-dimensional display. Further, when handling three-dimensional coordinates or the like in a three-dimensional space, using a three-dimensional display such as a DFD display device or a special input device is problematic in terms of cost.

  Therefore, an object of the present invention is to make it possible to easily and accurately specify a three-dimensional position in a three-dimensional space by specifying a two-dimensional position in the two-dimensional space. Another object of the present invention is to easily represent a three-dimensional shape by specifying a two-dimensional position in a two-dimensional space.

  The three-dimensional position designation device, the three-dimensional position designation method, the three-dimensional position designation program, the voxel modeling apparatus, the voxel modeling method, and the voxel modeling program according to the present invention employ the following means to achieve the above-described object. ing.

The three-dimensional position designation device according to the present invention is:
A three-dimensional position designation device for designating a three-dimensional position in a three-dimensional space,
Two-dimensional position specifying means for specifying a two-dimensional position in a two-dimensional space;
A two-dimensional position designated by the two-dimensional position designation means of the Nth stage Sherpinski carpet having an array of 8 ^N squares (where “N” is an integer equal to or greater than 1). Are associated with any one of 2 ^N × 2 ^N × 2 ^N voxels constituting a voxel space according to a predetermined correspondence rule, and the one region associated with the square region Computing means for obtaining a three-dimensional position in the three-dimensional space based on a position of the voxel in the voxel space;
Is provided.

The present inventors have intensively studied to make it possible to specify a three-dimensional position in a three-dimensional space easily and accurately, and as a result, a Sherpinsky carpet, which is one of fractals, and a set of a plurality of voxels. I came to pay attention to the voxel space. The Sherpinski carpet divides one square area into nine equal parts, and the process of generating an array of eight square areas using the central square area as a blank area (fractal expansion) excludes square areas that are blank areas. It is a fractal with self-similarity obtained by sequentially applying to a square region. That is, the square area of 1 is the initiator (8 ⁰⁾ the fractal expand one blank area and 8 the (first stage of the fractal development) is performed on the square area (8 ¹⁾ sequence is generated in eight When the fractal deployed for each square area (second stage of the fractal development) is performed 64 (8 ²⁾ sequences of the square area of excluding the blank area (and ^one blank area new 8) is generated, further, when the fractal expansion for each 64 square area except for the blank region (third stage of the fractal development) is performed 512 (8 ³ ) sequence of the square area (and new 8 ^two blank areas) will occur in the. In other words, when fractal expansion is performed N times by dividing a square area into 9 equal parts and generating an array of 8 square areas with the central square area as a blank area, 8 ^N pieces having self-similarity A Sherpinsky carpet having an array of square areas and Σ8 ⁿ⁻¹ (1 ≦ n ≦ N) blank areas is obtained. In this specification, a Shelpinsky carpet having an array of 8 ^N square regions and Σ8 ^n-1 (1 ≦ n ≦ N) blank regions is referred to as “the Nth stage Sherpinski Carpet. In addition, one is an initiator of the square area of (8 ⁰⁾ referred to as "the 0-th stage of the Sierpinski Carpet". On the other hand, considering the voxel space, one ^{(2 0 × 2 0 × 2} 0 = 8 0 pieces) Total number of voxels if divided into three-dimensional voxels 2 ¹ × 2 ¹ × is the minimum unit of theoretical 2 ¹ = 8 ¹ and it becomes the total number of voxels if divided into three dimensions each of the eight voxel 2 ² × 2 ² × 2 ² = 8 ² pieces and become, further, each of these 64 voxels the total number of voxels if divided into three dimensions become ^{2 3 × 2 3 × 2 3} = 8 3 pieces. That is, if the three-dimensional division (high resolution) of the voxel is executed N times, the total number of voxels in the volume data is 2 ^N × 2 ^N × 2 ^N = 8 ^N , which is the Nth stage shell It corresponds to the total number of square areas on the Pinsky carpet.

Thus, the present inventors have found commonality between the characteristics of the Shelpinsky carpet and the characteristics of a voxel space composed of a plurality of voxels, and using the commonality, the three-dimensional position in the three-dimensional space is found. Is to be specified. That is, the three-dimensional position specifying apparatus according to the present invention predetermines a square area corresponding to the two-dimensional position specified on the two-dimensional space of the Nth stage Sherpinski carpet having an array of 8 ^N square areas. Is associated with any one of 2 ^N × 2 ^N × 2 ^N voxels constituting the voxel space in accordance with the correspondence rule of and based on the position in the voxel space of one voxel associated with the square region A three-dimensional position in the three-dimensional space is acquired. Thus, if a two-dimensional position (for example, a two-dimensional coordinate) is specified in a two-dimensional space (for example, a two-dimensional coordinate system), the two-dimensional specified in the two-dimensional space by a simple arrangement calculation without specifying a depth. A position in the voxel space of one voxel corresponding to the position is acquired, and a three-dimensional position (for example, three-dimensional coordinates) in a three-dimensional space (for example, a three-dimensional coordinate system) is acquired from the position in the voxel space of the one voxel. Will be. Therefore, according to the three-dimensional position specifying apparatus according to the present invention, it is possible to easily and accurately specify a three-dimensional position in the three-dimensional space while reducing the calculation load by specifying the two-dimensional position in the two-dimensional space. It becomes. The “voxel” may basically be a simple cube having no so-called voxel value. However, a voxel value may be given to the voxel. In this case, by specifying a two-dimensional position in the two-dimensional space, a voxel value at a three-dimensional position corresponding to the two-dimensional position can be accessed. It becomes possible. Further, the N-th stage Sherpinski carpet may be directly associated with the two-dimensional space, or indirectly associated with a predetermined transformation.

The correspondence rule defines the correspondence between the eight square areas constituting the first Shelpinski carpet and the 2 × 2 × 2 voxels constituting one volume. Alternatively, the computing means may calculate a square area corresponding to the designated two-dimensional position of the Sherpinsky carpet in the nth stage (where “n” is an integer satisfying 1 ≦ n ≦ N). In a voxel space composed of 2 ⁿ × 2 ⁿ × 2 ⁿ voxels based on the position in the square area corresponding to the designated two-dimensional position of the n-1th Sherpinski carpet and the corresponding rule. The position in the voxel corresponding to the specified two-dimensional position in the voxel space composed of 2 ^n-1 × 2 ^n-1 × 2 ^n-1 voxels of the voxel corresponding to the specified two-dimensional position Acquired, A three-dimensional position in the three-dimensional space may be acquired based on the acquired positions of n voxels. As described above, if the correspondence relationship between the eight square regions constituting the first stage Sherpinski carpet and the 2 × 2 × 2 voxels constituting one volume is determined in advance, it is a fractal. By performing iterative calculation using the self-similarity of the Sherpinski carpet, it is possible to designate a three-dimensional position in a three-dimensional space at a high speed with a smaller calculation load.

  Further, the correspondence rule is that the eight square areas of the first-stage Sherpinski carpet are assigned to 2 × 2 × 2 voxels according to the order of the one-stroke path defined for them. The rule may be assigned so as to follow a one-stroke path. As a result, the adjacency relationship between at least two square regions in the N-th stage Sherpinski carpet can be maintained in the voxel space (three-dimensional space), and the proximity relationship of the two-dimensional positions in the two-dimensional space is 3. It can be kept relatively good even in a dimensional space.

  Further, the calculation means may be capable of setting a straight line or a broken line passing through the plurality of three-dimensional positions when a plurality of three-dimensional positions are designated in the three-dimensional space. Furthermore, the calculation means may be capable of setting curves determined from the three or more three-dimensional positions when three or more three-dimensional positions are designated in the three-dimensional space. The computing means may be capable of setting a plane determined from the three or more three-dimensional positions when three or more three-dimensional positions are designated in the three-dimensional space. Furthermore, the calculation means may be capable of setting curved surfaces determined from the four or more three-dimensional positions when four or more three-dimensional positions are designated in the three-dimensional space. The computing means may be capable of setting a circle or a sphere based on the two-dimensional three-dimensional positions when two three-dimensional positions are designated in the three-dimensional space. This makes it possible to draw and design various three-dimensional shapes using the three-dimensional position specifying apparatus according to the present invention.

  The three-dimensional position specifying device displays a display unit capable of displaying an image on a display screen, and displays an image based on the Nth stage Sherpinski carpet on the display screen, and the calculation unit Display control means for plotting and displaying three-dimensional coordinates indicating the acquired three-dimensional position on the display screen may be provided. This makes it possible to designate a two-dimensional position, that is, a square region of the Nth stage Sherpinski carpet while referring to a point indicating three-dimensional coordinates on the display screen. The dimension position can be easily specified.

  The display control unit plots and displays the three-dimensional coordinates indicating the three-dimensional position acquired by the calculation unit on the display screen, and displays an image based on a voxel having a predetermined size around the three-dimensional position. It may be allowed. As a result, it is possible to easily grasp where in the three-dimensional space the three-dimensional position corresponding to the two-dimensional position designated using the two-dimensional position designation means is located.

The three-dimensional position designation method according to the present invention includes:
A three-dimensional position designation method for designating a three-dimensional position in a three-dimensional space,
(A) identifying a specified two-dimensional position in a two-dimensional space;
(B) The two-dimensional position specified in step (a) of the N-th stage Sherpinski carpet having an array of 8 ^N square areas (where “N” is an integer greater than or equal to 1). Are associated with any one of 2 ^N × 2 ^N × 2 ^N voxels constituting a voxel space according to a predetermined correspondence rule, and the one region associated with the square region Obtaining a three-dimensional position in the three-dimensional space based on a position of the voxel in the voxel space;
Is included.

  In this method, when a two-dimensional position is specified in the two-dimensional space, even if the depth is not specified, a voxel space of one voxel corresponding to the two-dimensional position specified in the two-dimensional space by simple arrangement calculation. Is obtained, and the three-dimensional position in the three-dimensional space is obtained from the position of the one voxel in the voxel space. Therefore, according to this method, by specifying the two-dimensional position in the two-dimensional space, the three-dimensional position in the three-dimensional space can be specified easily and accurately while reducing the calculation load.

The three-dimensional position designation program according to the present invention is:
A three-dimensional position designation program that causes a computer to function as a device for designating a three-dimensional position in a three-dimensional space,
A two-dimensional position specifying module for specifying a two-dimensional position specified in a two-dimensional space;
A square area corresponding to the specified two-dimensional position of the N-th stage Sherpinski carpet having an array of 8 ^N square areas (where “N” is an integer equal to or greater than 1) Corresponding to any one of 2 ^N × 2 ^N × 2 ^N voxels constituting the voxel space according to the correspondence rule, and at the position of the one voxel associated with the square region in the voxel space An arithmetic module that obtains a three-dimensional position in the three-dimensional space based on;
Is provided.

  In a computer in which this program is installed, if a two-dimensional position (for example, xy coordinates) is specified in the two-dimensional space, the two-dimensional position specified in the two-dimensional space can be obtained by simple arrangement calculation without specifying the depth. The position of the corresponding one voxel in the voxel space is acquired, and the three-dimensional position in the three-dimensional space is acquired from the position of the one voxel in the voxel space. Therefore, according to this program, by specifying the two-dimensional position in the two-dimensional space, it is possible to easily and accurately specify the three-dimensional position in the three-dimensional space while reducing the calculation load.

The voxel modeling apparatus according to the present invention is:
A voxel modeling device capable of expressing a three-dimensional shape as a set of voxels,
Two-dimensional position specifying means for specifying a two-dimensional position in a two-dimensional space;
A two-dimensional position designated by the two-dimensional position designation means of the Nth stage Sherpinski carpet having an array of 8 ^N squares (where “N” is an integer equal to or greater than 1). Are associated with any one of 2 ^N × 2 ^N × 2 ^N voxels constituting a voxel space according to a predetermined correspondence rule, and the one region associated with the square region Position acquisition means for acquiring a position of the voxel in the voxel space;
Shape setting means for setting a three-dimensional shape based on voxels at positions acquired by the position acquisition means;
Is provided.

  In this voxel modeling apparatus, when a two-dimensional position is specified in a two-dimensional space, the position in the voxel space of one voxel corresponding to the two-dimensional position specified in the two-dimensional space is acquired by simple arrangement calculation, The three-dimensional shape is set by erasing the voxel at the acquired position from the voxel space or arranging the voxels at the acquired position in the three-dimensional space. Therefore, according to this voxel modeling apparatus, a three-dimensional shape can be easily expressed by specifying a two-dimensional position in a two-dimensional space.

The voxel modeling method according to the present invention includes:
A voxel modeling method for expressing a three-dimensional shape as a set of voxels,
(A) identifying a specified two-dimensional position in a two-dimensional space;
(B) The two-dimensional position specified in step (a) of the N-th stage Sherpinski carpet having an array of 8 ^N square areas (where “N” is an integer greater than or equal to 1). Are associated with any one of 2 ^N × 2 ^N × 2 ^N voxels constituting a voxel space according to a predetermined correspondence rule, and the one region associated with the square region Obtaining a position of the voxel in the voxel space;
(C) setting a three-dimensional shape based on the voxels at the position acquired in step (b);
Is included.

  In this method, when a two-dimensional position is specified in the two-dimensional space, a position in the voxel space of one voxel corresponding to the two-dimensional position specified in the two-dimensional space is acquired by simple arrangement calculation, The three-dimensional shape is set by erasing the voxel at the acquired position from the voxel space or arranging the voxels at the acquired position in the three-dimensional space. Therefore, according to this method, a three-dimensional shape can be easily expressed by specifying a two-dimensional position in a two-dimensional space.

The program for voxel modeling according to the present invention is:
A voxel modeling program for causing a computer to function as a device for expressing a three-dimensional shape as a set of voxels,
A two-dimensional position specifying module for specifying a two-dimensional position specified in a two-dimensional space;
A two-dimensional position designated by the two-dimensional position designation means of the Nth stage Sherpinski carpet having an array of 8 ^N squares (where “N” is an integer equal to or greater than 1). Are associated with any one of 2 ^N × 2 ^N × 2 ^N voxels constituting a voxel space according to a predetermined correspondence rule, and the one region associated with the square region A position acquisition module that acquires a position of the voxel in the voxel space; a shape setting module that sets a three-dimensional shape based on the voxel at the position acquired by the position acquisition module;
It is to be prepared.

  In a computer in which this program is installed, when a two-dimensional position is specified in a two-dimensional space, the position in the voxel space of one voxel corresponding to the two-dimensional position specified in the two-dimensional space is acquired by simple arrangement calculation. In addition, the three-dimensional shape is set by erasing the voxel at the acquired position from the voxel space or arranging the voxels at the acquired position in the three-dimensional space. Therefore, according to this program, it is possible to easily represent a three-dimensional shape by specifying a two-dimensional position in a two-dimensional space.

  Next, the best mode for carrying out the present invention will be described with reference to examples.

  FIG. 1 is a schematic configuration diagram of a computer 20 as a three-dimensional position specifying apparatus according to an embodiment of the present invention. As shown in the figure, the computer 20 of the embodiment includes a CPU, ROM, RAM, graphic processor (GPU), graphic memory (VRAM), system bus, various interfaces, hard disk drive and flash memory drive (SSD) (not shown). The computer is configured as a general-purpose computer including an external storage device or the like, and is used by being connected to a display device 30 such as a liquid crystal display which is a general two-dimensional display, a keyboard 40 or a mouse 50 as an input device, and the like. Then, the computer 20 is designated with a two-dimensional position (two-dimensional coordinate) in a two-dimensional space (two-dimensional coordinate system) displayed on the display screen 31 of the display device 30 to specify a three-dimensional space (three-dimensional coordinate system). A three-dimensional position designation program that enables designation of a three-dimensional position (three-dimensional coordinates) is installed. In the following description, “2D” is appropriately referred to as “2D”, and “3D” is referred to as “3D”.

  When the three-dimensional position designation program is started in the computer 20, a window 90 is displayed on the display screen 31 of the display device 30 as shown in FIGS. The window 90 includes a 2D coordinate designation area 92 and a 3D image display area 93. In the 2D coordinate designation area 92 as a two-dimensional space, fractal expansion for generating an array of eight square areas by dividing one square area into nine equal parts and using the central square area as a blank area N times (however, “ N ″ is an integer greater than or equal to the value 1. In the embodiment, for example, N = 5.) The N-th stage Sherpinski carpet 100, which is a fractal obtained by application, is displayed. In the 3D image display area 93, a cubic three-dimensional frame XYZ indicating a three-dimensional space is displayed.

  When the user of the computer 20 uses the mouse 50 or the keyboard 40 to place a cursor on a square area (an area not painted black in the figure) on the Sherpinski carpet 100 displayed in the 2D coordinate designation area 92, 3D A point P indicating 3D coordinates corresponding to the cursor position is displayed in the 3D frame XYZ of the image display area 93, and a cubic frame F is displayed around the point P indicating the 3D coordinates. When the user moves the cursor on the Shelpinski carpet 100, the point P and the frame F are displayed so as to move in the three-dimensional frame XYZ according to the position of the cursor. When the user performs a 2D position determination process such as clicking the mouse 50 with the cursor placed on the square area on the Sherpinski carpet 100, a location corresponding to the cursor position on the Sherpinski carpet 100 is displayed. A point is plotted and displayed at a point (see a part indicated by an arrow in FIG. 2), and a point (hereinafter referred to as “determined point”) Pc indicating a three-dimensional coordinate corresponding to the cursor position in the three-dimensional frame XYZ is fixedly displayed. The frame F is erased. Note that the three-dimensional frame XYZ, the fixed point Pc, and the like can be moved in the 3D image display area 93 by a user operation.

  The window 90 includes buttons 95 such as “LINE”, “CURVE”, “PLANE”, “CURVED SURFACE”, “CIRCLE”, “SPHERE”, “delete”, “copy”, “tool”, “save”. Is arranged. The “LINE” button is used to instruct the setting of a straight line or a broken line passing through a plurality of fixed points Pc existing in the three-dimensional frame XYZ. The “CURVE” button is used to instruct the setting of a curve determined from three or more fixed points Pc existing in the three-dimensional frame XYZ. The “PLANE” button is used to instruct the setting of a plane determined from three or more fixed points Pc existing in the three-dimensional frame XYZ. The “CURVED SURFACE” button is used to instruct the setting of a curved surface determined from four or more fixed points Pc existing in the three-dimensional frame XYZ. The “CIRCLE” button is used to instruct the setting of a circle (plane) centered on one of the two fixed points Pc existing in the three-dimensional frame XYZ and the other one on the circumference. is there. The “SPHERE” button is used to instruct the setting of a spherical surface centered on one of the two fixed points Pc existing in the three-dimensional frame XYZ and the other one on the spherical surface. The “delete” button is used to instruct the deletion of the fixed point Pc, line, surface, etc. existing in the three-dimensional frame XYZ. The “copy” button is used to instruct copying of a figure such as a line or a surface existing in the three-dimensional frame XYZ. The “tool” button is capable of instructing execution of an option prepared in advance (for example, setting of a vector field described later). The “save” button is used to instruct the saving of the three-dimensional shape displayed in the three-dimensional frame XYZ.

  When the three-dimensional position designation program is activated, the computer 20 is installed with hardware such as a CPU, a ROM, a RAM, a GPU, various interfaces, and an external storage device, as shown in FIG. The input receiving unit 21, the information storage unit (RAM and external storage device) 22, the modeling unit 23, the display control unit 24, and the like are constructed as functional blocks in cooperation with one or both of the dimension position specifying programs. The input reception unit 21 receives a 2D position designated by the user, that is, a cursor position in the 2D coordinate designation area 92 (xy coordinates in pixel units in the two-dimensional absolute coordinate system set on the display screen 31) from the mouse 50 and the keyboard 40. The input of information is received, and the received information is stored in the information storage unit (RAM) 22. The modeling unit 23 calculates the 3D coordinates in the three-dimensional frame XYZ corresponding to the cursor position based on the cursor position in the 2D coordinate designation area 92 designated by the user, or operates the button 95 on the window 90 described above. Set lines, surfaces, etc. accordingly. The display control unit 24 executes image display processing (including rendering) in accordance with a user operation in the 2D coordinate designation area 92 and the 3D image display area 93.

  Next, a procedure for displaying the point P in the three-dimensional frame XYZ as a three-dimensional space and setting the fixed point Pc using the computer 20 in which the three-dimensional position designation program is installed will be described. FIG. 3 is a flowchart illustrating an example of a 3D coordinate setting routine executed in the computer 20 according to the embodiment. In this 3D coordinate setting routine, when the three-dimensional position designation program is started and the cursor is placed on the square area on the Sherpinski carpet 100 displayed in the 2D coordinate designation area 92, for example, the modeling unit 23 of the computer 20 is used. Is repeatedly executed.

  At the start of the 3D coordinate setting routine of FIG. 3, the modeling unit 23 converts the cursor position (xy coordinates in pixel units on the display screen 31) in the 2D coordinate specification area 92 specified by the user, thereby converting the 2D coordinate specification area. 2D coordinates (x, y) in the two-dimensional absolute coordinate system set to 92 are acquired (step S100). After the processing of step S100, the modeling unit 23 performs predetermined coordinates (x (n), y (n)), coordinates (x ″ (n), y ″ (n)), and coordinates (X ′ (n), Y ′ (n), Z ′ (n)) are initialized according to the following equations (1) to (3) (step S110). However, “n” is a control variable. Then, the modeling unit 23 executes a coordinate conversion process for converting 2D coordinates (x, y) into 3D coordinates (X, Y, Z) in the three-dimensional frame XYZ using a table based on a predetermined correspondence rule. (Step S120).

(x (0), y (0)) = (x, y) (1)
(x ″ (0), y ″ (0)) = (0, 0)… (2)
(X '(0), Y' (0), Z '(0)) = (0, 0, 0) ... (3)

  The correspondence rule used in the coordinate transformation process in step S120 is the correspondence between the eight square areas constituting the first Shelpinsky carpet and the 2 × 2 × 2 = 8 voxels constituting one volume. It defines the relationship. That is, in the embodiment, as shown in FIG. 4, the X direction from a predetermined base point (for example, the vertex at the lower left in the figure) with respect to the eight square regions constituting the first stage Sherpinski carpet → A two-dimensional one-stroke path (circular path) traveling in the Y direction, −X direction, and −Y direction is determined in advance, and a predetermined base point (for example, in the figure) is set for 2 × 2 × 2 voxels. A three-dimensional one-stroke path that proceeds in the x direction → z direction → −x direction → y direction → x direction → −z direction → −x direction → −y direction is determined in advance. The correspondence rule is that the eight-dimensional area of the Sherpinski carpet in the first stage is applied to the 3D stroke for 2 × 2 × 2 voxels according to the order in the path of the 2D stroke stroke. It is supposed to be assigned so as to follow the path of writing. In the embodiment, the table shown in FIG. 5 is prepared in order to apply the correspondence rule to the coordinate conversion process. In this table, as the 2D positions of the eight square areas constituting the first stage Sherpinski carpet, each square area has a left top vertex (hereinafter referred to as “origin” of the square area) in FIG. (0,0), (1,0), (2,0), (2,1), (2,2), (1,2), (0,2), (0,1) Relative coordinates are given, and 2 × 2 × 2 = 8 voxel 3D positions are set to (0, 0, 0, 0, 0, 0) on the lower left apex of each voxel in FIG. 0), (1, 0, 0), (1, 0, 1), (0, 0, 1), (0, 1, 1), (1, 1, 1), (1, 1, 0) , (0, 1, 0) three-dimensional relative coordinates are assigned, and the 2D position (relative coordinates) of the square area of the Sherpinski carpet and eight The 3D positions (relative coordinates) of the cels are associated as shown in FIG.

By using the table shown in FIG. 5, 2 ^N constituting the voxel space square region Sierpinski Carpet of the N stage corresponding to the 2D coordinates (x, y) as shown in FIGS. 6 and 7 It can be associated with any one of × 2 ^N × 2 ^N voxels. In the following description, the value N is appropriately referred to as “resolution” of the Sherpinski carpet or voxel space. 6 and 7 exemplify the case where the resolution N of the Sherpinski carpet 100 displayed in the 2D coordinate designation area 92 is a value 3, and the cursor is at the position shown in FIG. And In this case, if it is assumed that the first-stage Shelpinsky carpet is displayed in the 2D coordinate designation area 92, as can be seen from FIG. 6, the 2D coordinates (x, y) are obtained from the correspondence rule shown in FIG. It will be included in the sixth square area of the first stage Sherpinski carpet. Thus, one is the initiator of the origin O ₁ of the 6 th square area (8 ⁰⁾ the relative coordinates in the square region (zeroth stage of the Sierpinski Carpet) of (origin O ₀ a (0, 0) 5), using the table of FIG. 5, 2D coordinates (x, y) in a voxel space composed of 2 ¹ × 2 ¹ × 2 ¹ = 8 voxels (a voxel space of resolution N = 1) 2 ⁰ × voxels corresponding to) 2 ⁰ × 2 ⁰ = 1 single 2D coordinates in the voxel space composed of voxels (x, can be obtained relative coordinates in the voxel corresponding to y) (FIGS. 7 (a) reference).

Further, assuming that the second-stage Shelpinsky carpet is displayed in the 2D coordinate designation area 92, as can be seen from FIG. 6, the 2D coordinates (x, y) are as described above according to the correspondence rule shown in FIG. Of the eight square areas constituting the sixth square area in the first stage Sherpinski carpet, the seventh square area is included. Therefore, if the relative coordinates (the origin O ₁ is (0, 0)) of the sixth square area of the first stage Sherpinski carpet of the origin O ₂ of the seventh square area are obtained, by using the table of FIG. ^{5, 2 2 × 2 2 ×} 2 2 pieces = 64 voxel space (resolution N = 2 of the voxel space) in a 2D coordinate consisting of voxels (x, y) resolution corresponding to N = Relative coordinates in voxels corresponding to 2D coordinates (x, y) can be obtained within one voxel space (see FIG. 7B).

The same applies to the 2D coordinates (x, y) of the (n-1) th stage Sherpinski carpet corresponding to the 2D coordinates (x, y) of the nth stage Sherpinski carpet. When the relative coordinates (position) in the square area are obtained, the relative coordinates of the square area are determined using the table of FIG. 5 in the voxel resolution N = n and the voxel resolution N corresponding to the 2D coordinates (x, y). Can be converted into relative coordinates in the voxel corresponding to the 2D coordinate (x, y) in the n-1 voxel space (see FIG. 7C). If a three-dimensional frame XYZ as a three-dimensional space is associated with a voxel space of resolution N and the three-dimensional frame XYZ is divided into 2 ^N × 2 ^N × 2 ^N voxels, 3D coordinates (X, Y, Z) in the three-dimensional frame XYZ corresponding to the 2D coordinates (x, y) can be obtained by adding the relative coordinates of the voxels in the respective steps.

FIG. 8 is a flowchart showing an example of the coordinate conversion process in step S120 for converting 2D coordinates (x, y) into 3D coordinates (X, Y, Z) in the three-dimensional frame XYZ by the above-described procedure. As shown in FIG. 8, at the start of the coordinate conversion process, the modeling unit 23 sets the variable n to the value 1 (step S1200), and the coordinates (x (n), y (n)) are expressed by the following formula ( Set according to 4) and (5) (step S1210). In equations (4) and (5), “s” indicates the length (number of pixels) of one side of the Sherpinski carpet 100 displayed in the 2D coordinate designation area 92 (see FIG. 2). Next, values x ′ (n) and y ′ (n) are calculated from the following equations (6) and (7) using the set coordinates (x (n), y (n)) (step S1220). The coordinates (x ″ (n), y ″ (n)) are set by truncating the decimal places of x ′ (n) and y ′ (n), respectively (step S1230). Here, the coordinates (x (n), y ( n)) is, 2D coordinates relative to the origin O _n square area corresponding to the Sierpinski Carpet of 2D coordinates of the n steps (x, y) (x, y ) Is the absolute coordinate of the point. Further, the coordinates (x ″ (n), y ″ (n)) obtained through the processes of steps S1210 and S1220 are square areas corresponding to the 2D coordinates (x, y) of the n-th Sherpinski carpet. indicating the origin O _n (n-1) th stage of the Sierpinski carpet of 2D coordinates (x, y) of the relative coordinates in the square region corresponding to.

x (n) = x (n-1) -3 ^n-1 / s · x ″ (n-1) (4)
y (n) = y (n-1) -3 ^n-1 / s · y ″ (n-1) (5)
x ′ (n) = 3 ⁿ / s · x (n) (6)
y ′ (n) = 3 ⁿ / s · y (n) (7)

By the processing in step S1230, the coordinates (x ″ (n), y ″ (n)) are obtained as any of the two-dimensional relative coordinates in the table of FIG. 5, and therefore the coordinates (x ″ (n ), Y ″ (n)) corresponding to the three-dimensional relative coordinates (X ″ (n), Y ″ (n), Z ″ (n)), that is, 2D coordinates (x, y) in the voxel space of resolution n. The relative coordinates in the voxel corresponding to the 2D coordinate (x, y) in the voxel space with the resolution n−1 of the voxel corresponding to can be derived (step S1240). When (n), Z ″ (n)) is obtained, 2D coordinates (x, y) are obtained in a voxel space composed of 2 ⁿ × 2 ⁿ × 2 ⁿ voxels according to the following equations (8) to (10). The coordinates (X ', Y', Z ') of the origin of the voxel corresponding to Step S1250). After the process of step S1250, it is determined whether or not the variable n matches the value N (the resolution of the Sherpinski carpet 100) (step S1260). If the variable n is less than the value N, the variable n is set. Increment (step S1270), the processing of steps S1210 to S1250 is executed again. In step S1260, when the variable n matches the value N, the 3D coordinates (X, Y, Z) corresponding to the 2D coordinates (x, y) based on the coordinates (X ′, Y ′, Z ′). And is stored in the information storage unit 22 (RAM) (step S1280). In step S1280 of the embodiment, 2D coordinates are obtained in a voxel space composed of 2 ^N × 2 ^N × 2 ^N voxels obtained from coordinates (X ′, Y ′, Z ′) according to the following equations (11) to (13). The coordinates of the center of the voxel corresponding to (x, y) are set as 3D coordinates (X, Y, Z). However, in equations (11) to (13), “S” indicates the length (number of pixels) of one side of the three-dimensional frame XYZ displayed in the 3D image display area 93 (see FIG. 2).

X ′ = X ′ + 2 ^Nn · X (n) (8)
Y ′ = Y ′ + 2 ^Nn・ Y (n) (9)
Z ′ = Z ′ + 2 ^Nn・ Z (n) (10)
X = X ′ + S / 2 ^{N + 1} (11)
Y = Y '+ S / 2 ^{N + 1} (12)
Z = Z '+ S / 2 ^{N + 1} (13)

When the 3D coordinates (X, Y, Z) are set as described above, the modeling unit 23 causes the cubic frame F (eight vertices and vertices) having a predetermined size centered on the 3D coordinates (X, Y, Z). (12 straight lines connecting each other) and the set information are stored in the information storage unit 22 (RAM) (step S130), and the point P and the frame F corresponding to the set 3D coordinates (X, Y, Z) Is displayed to the display control unit 24 (step S140). In the embodiment, the size of the frame F set in step S130 is that the three-dimensional frame XYZ is divided into 2 ^m × 2 ^m × 2 ^m (where m <N, for example, m = 2) voxels. Coincides with the size of one voxel at a time. In addition, the display control unit 24 that has received the image display command from the modeling unit 23 reads information on the 3D coordinates (X, Y, Z), the frame F, and the like from the information storage unit 22 so that the point P and the frame F are 3 in number. The image display process is executed so that the 3D image display area 93 is projected and displayed together with the dimension frame XYZ, the existing fixed point Pc, and the like. After the process of step S140, the modeling unit 23 determines whether or not the 2D position determination process has been executed by the user (step S150). If the 2D position determination process has not been executed, the modeling unit 23 again performs step S100. The subsequent processing is executed.

  When the 2D position determination process is executed by the user, the modeling unit 23 uses the 3D coordinates (X, Y, Z) set in step S120 (S1280) as the coordinates of the new determined point Pc. After storing the data in the storage unit 22 (RAM) (step S160), the display control unit 24 is instructed to display an image such as a fixed point Pc (step S170), and the processing after step S100 is executed again. Upon receiving the image display command from the modeling unit 23, the display control unit 24 reads the 3D coordinates (X, Y, Z) and the like of the fixed point Pc from the information storage unit 22, and the new fixed point Pc is displayed in the three-dimensional frame XYZ. The image display processing is executed so that the image is projected and displayed on the 3D image display area 93 together with the existing fixed point Pc and the like. Note that the pre-determined point P and the definite point Pc may be displayed in the 3D image display area 93 by changing the color or shape in consideration of distinguishability.

  Next, a procedure for setting lines, planes, and the like in the three-dimensional frame XYZ as a three-dimensional space using the computer 20 in which the three-dimensional position designation program is installed will be described with reference to FIG. FIG. 9 is a flowchart illustrating an example of a 3D drawing routine executed by the computer 20 according to the embodiment. The 3D drawing routine includes buttons 95 such as “LINE”, “CURVE”, “PLANE”, “CURVED SURFACE”, “CIRCLE”, and “SPHERE” on the window 90 in a state in which the three-dimensional position designation program is activated. Is clicked, it is executed by the modeling unit 23 of the computer 20.

  At the start of the 3D drawing routine of FIG. 9, the modeling unit 23 determines that the button 95 clicked by the user is one of “LINE”, “CURVE”, “PLANE”, “CURVED SURFACE”, “CIRCLE”, and “SPHERE”. To determine the drawing target corresponding to the button 95 clicked by the user (step S200). Next, the 3D coordinates (X, Y, Z) of all the fixed points Pc are read from the information storage unit 22 (step S210), and it is determined whether or not the drawing target specified by the user can be drawn (step S220). ). In step S220, it is basically determined whether or not the drawing target can be drawn by comparing the minimum number of fixed points Pc determined for each drawing target with the number of existing fixed points Pc. . For example, in the case where the drawing of a curved surface is specified even though there are only two fixed points Pc, a negative determination is made in step S220, and the modeling unit 23 determines, for example, “3D position. Instruct the display control unit 24 to display an “ERROR” message on the display screen 31 (step S250).

  On the other hand, if it is determined in step S220 that the drawing target specified by the user can be drawn, the modeling unit 23 determines the straight line specified by the user based on the 3D coordinates (X, Y, Z) of the fixed point Pc, A polygonal line, a curve, a plane, a curved surface, a circle, or a sphere is set, and the set information is stored in the information storage unit 22 (step S230). Then, the modeling unit 23 instructs the display control unit 24 to display an image of the set line or surface (step S240), and ends this routine. Upon receiving the image display command from the modeling unit 23, the display control unit 24 displays the image so that the set line or surface is projected and displayed on the 3D image display area 93 together with the 3D frame XYZ, the existing fixed point Pc, or the like. Execute the process.

In the process of step S240, when there are two definite points Pc, the two definite points Pc can be expressed as (X ₀ , Y ₀ , Z ₀ ) and (X ₁ , Y ₁ , Z ₁ ), respectively. For example, a straight line passing through these two fixed points Pc can be defined as in the following equation (14). In addition, as a curve determined from three or more fixed points Pc, parametrics such as a Bezier curve and a NURBS curve can be used. Here, when N definite points Pc exist, if the parameter is t and the order of the curve is n, the 3D coordinate P (t) on the Bezier curve is expressed by the following equation (15). Can be defined. Further, when N definite points Pc exist, if f _{i, k} (t) is a B-spline basis function, w _i is a weight, and the order of the curve is n, 3D on the NURBS curve The coordinate P (t) can be defined as the following equation (16). Further, when there are three definite points Pc, any one of the three definite points Pc is set to (X ₀ , Y ₀ , Z ₀ ), and a normal vector determined from the three definite points Pc is (a , B, c), a plane determined from the three definite points Pc can be defined as the following equation (17). As a curved surface determined from four or more definite points Pc, a parametric curved surface such as a Bezier curved surface defined by the following equation (18) or a NURBS curved surface defined by the following equation (19) can be used (however, In equations (18) and (19), “u” and “v” are parameters.)

  As described above, the computer 20 in which the three-dimensional position designation program of the embodiment is installed is connected to the display device 30 capable of displaying an image on the display screen 31, and the three-dimensional position designation program is started. Then, the display control unit 24 causes the N-th stage Shelpinski carpet 100 to be displayed in the 2D coordinate designation area 92 as a two-dimensional space on the display screen 31. Thus, when the 2D position (xy coordinates in pixel units), that is, any square area is designated on the N-th stage Sherpinski carpet 100 displayed in the 2D coordinate designation area 92, the depth is not designated. The position in the voxel space with the resolution N of one voxel corresponding to the 2D position (2D coordinates (x, y)) designated on the Sherpinski carpet 100 is obtained by simple arrangement calculation. Then, 3D coordinates (X, Y, Z) that are three-dimensional positions in the three-dimensional frame XYZ as a three-dimensional space are acquired from the position of the one voxel in the voxel space, and the three-dimensional coordinates (X, Y, Z, A point P indicating Z) is plotted and displayed in the 3D image display area 93 on the display screen 31.

  As described above, if the computer 20 in which the three-dimensional position specifying program is installed is used, the 3D coordinates (3D positions) in the three-dimensional frame XYZ are reduced while the calculation load is reduced by specifying the 2D positions in the 2D coordinate specifying area 92. Can be specified easily and accurately. Further, the computer 20 can designate the 2D position, that is, the square area of the N-th stage Shelpinski carpet 100 with reference to the point P plotted in the 3D image display area 93, so that the 3D frame is displayed. It becomes possible to easily specify desired 3D coordinates in XYZ. Further, since the 3D image display area 93 displays a cubic frame F based on voxels of a predetermined size around the point P corresponding to the 3D coordinates until the 2D position determination process is executed. It is possible to easily grasp where in the three-dimensional frame XYZ the 3D coordinates (point P) corresponding to the 2D position designated in the coordinate designation area 92 are located.

  Further, the correspondence rule applied to the computer 20 of the embodiment is the correspondence between the eight square areas constituting the first Shelpinsky carpet and the 2 × 2 × 2 voxels constituting one volume. It defines the relationship. Accordingly, the 2D coordinates (x, y) of the (n−1) th Sherpinski carpet in the square region corresponding to the 2D coordinates (x, y) of the Shelpinski carpet of the nth stage (1 ≦ n ≦ N). From the relative coordinates (x ″ (n), y ″ (n)) in the square region corresponding to y) and the table of FIG. 5 based on the above correspondence rules, 2D coordinates (x, The relative coordinates (X ″ (n), Y ″ (n), Z ″ (n) in the voxel corresponding to the 2D coordinate (x, y) in the voxel space with the resolution N = n−1 of the voxel corresponding to y) If the obtained n relative coordinates (X ″ (n), Y ″ (n), Z ″ (n)) are used, 2D coordinates (x, y) are supported. It is possible to acquire 3D coordinates (X, Y, Z) in the 3D frame XYZ To become. As described above, if the correspondence relationship between the eight square regions constituting the first stage Sherpinski carpet and the 2 × 2 × 2 voxels constituting one volume is determined in advance, it is a fractal. By executing repetitive calculation using the self-similarity of the Sherpinsky carpet, it is possible to specify 3D coordinates (X, Y, Z) in the three-dimensional frame XYZ at high speed with a smaller calculation load.

However, if the self-similarity of the Sherpinski carpet is used, it is not always necessary to display the Sherpinski carpet 100 having a relatively high resolution such as N = 5 in the 2D coordinate designation area 92. That is, a shellpinsky carpet 100 having a relatively small resolution (for example, N = 1 to 3) is displayed in the 2D coordinate designation area 92, and each time a 2D position, that is, a square area is designated, a new shellpinski carpet By displaying the carpet 100 in the 2D coordinate designation area 92 as a fractal expansion of the designated square area, the user can gradually set desired 3D coordinates (X, Y, Z) in the 3D frame XYZ. It can be specified. Further, as a table, a table that associates all square areas of the N-th stage Sherpinski carpet with 2 ^N × 2 ^N × 2 ^N voxels constituting the voxel space may be prepared in advance. Good.

Furthermore, the correspondence rule applied to the computer 20 of the embodiment is 2 × 2 according to the order of the eight square areas of the first-stage Sherpinski carpet in accordance with the order on the one-stroke path defined for them. This is a rule that assigns two voxels to follow a one-stroke path. As a result, the adjacent relationship between at least two square regions in the N-th stage Sherpinski carpet 100 can be maintained in a voxel space (3D frame XYZ) composed of 2 ^N × 2 ^N × 2 ^N voxels. Therefore, the proximity relationship of the square areas on the Sherpinski carpet 100 can be maintained relatively well even in the three-dimensional frame XYZ. However, the correspondence rule is that the 2 × 2 × 2 voxels constituting one volume in the three-dimensional space and the eight square areas constituting the first stage Sherpinski carpet in the two-dimensional space. Any correspondence relationship may be defined as long as it defines a correspondence relationship with the above.

  The modeling unit 23 constructed in the computer 20 of the embodiment passes through the plurality of 3D coordinates in response to the click of the “LINE” button when a plurality of 3D coordinates are designated in the three-dimensional frame XYZ. A straight line or a broken line can be set. Furthermore, when three or more 3D coordinates are specified in the three-dimensional frame XYZ, the modeling unit 23 can set a curve determined from the three or more 3D coordinates in response to a click on the “CURVE” button. . Further, when three or more 3D coordinates are specified in the three-dimensional frame XYZ, the modeling unit 23 can set a plane determined from the three or more 3D coordinates in response to a click on “PLANE”. Furthermore, the modeling unit 23 can set a curved surface determined from three or more 3D coordinates in response to a click of the “CURVED SURFACE” button when four or more 3D coordinates are specified in the three-dimensional frame XYZ. is there. In addition, when two 3D coordinates are specified in the three-dimensional frame XYZ, the modeling unit 23 makes a circle or a sphere based on the two 3D coordinates in response to the click of the “CIRCLE” button or the “SPHERE” button. Can be set. Therefore, if the computer 20 in which the three-dimensional position designation program of the embodiment is installed, various three-dimensional shapes can be drawn and designed. However, the setting procedure of the lines and planes is not limited to the procedure shown in FIG. 9, and after the user clicks the button 95, the required number of 3D positions (the square area of the Sherpinski carpet 100) are designated. The setting of the line and the surface may be executed after the process is performed.

  In the above embodiment, the display device 30 may be configured as a so-called liquid crystal tablet including a tablet capable of detecting absolute coordinates on the display screen 31 designated by a stylus (not shown). Also, a so-called dual monitor may be used as the display device 30, and the 2D coordinate designation region 92 may be displayed on one of the two display devices 30 and the 3D image display region 93 may be displayed on the other. Furthermore, in the above embodiment, the N-th stage Sherpinski carpet 100 is directly associated with the 2D coordinate designation area 92 as a two-dimensional space, but the present invention is not limited to this. That is, the N-th stage Sherpinski carpet 100 is indirectly connected through a further 2D coordinate conversion process so that the correspondence between the 2D coordinate designation area 92 and the three-dimensional frame 93 becomes more intuitive and easy to understand. May be associated. When the user places the cursor in the blank area of the Sherpinski carpet 100, a frame (image) based on the voxel corresponding to the square area to which the blank area belongs is displayed in the 3D image display area 93, Information related to the square area to which the blank area belongs may be displayed in the 2D coordinate designation area 92 or the 3D image display area 93.

  Next, an application example of the three-dimensional position designation apparatus and method and the three-dimensional position designation program according to the present invention, and the voxel modeling apparatus, voxel modeling method and voxel modeling program according to the present invention will be described.

  “Voxel” in the above embodiment basically means a simple cube having no so-called voxel value, but a voxel value is assigned to each voxel in a voxel space associated with a three-dimensional space. Also good. Thus, by specifying a two-dimensional position in the two-dimensional space, it becomes possible to access a voxel value at a three-dimensional position corresponding to the two-dimensional position. As an application example for giving a voxel value to a voxel in this way, there is a color picker that is an interface that allows a user to select an arbitrary color in photo processing software, paint software, or the like. That is, on the computer, the color is expressed by three components of R (red), G (green), and B (blue). For example, (R, G, B) = (0, 0, 0) is black, ( R, G, B) = (255, 0, 0) is red, (R, G, B) = (255, 255, 255) is white, and the intensity of each color component is expressed as a parameter of 256 gradations. It is common to be done. Therefore, on the computer, the color space can be regarded as a three-dimensional space composed of RGB three axes.

Based on this, 2 ⁸ × 2 ⁸ × 2 ⁸ voxels (each storing RGB color information respectively) constituting the square region and voxel space of the Sherpinsky carpet with resolution N = 8 (8th stage). 3), or by using one of the correspondence rules as described above, by designating any square area of the Shelpinsky carpet with resolution N = 8, It is possible to specify (acquire) RGB color information in the color space. Note that the same color picker as in the RGB format can be configured using the present invention for an HDR (High Dynamic Range) format that expresses color components using floating-point numbers instead of 256 gradations. Furthermore, the YUV format that expresses the color by the three information of the luminance signal (Y), the difference between the luminance signal and the blue component (U), and the difference between the luminance signal and the red component (V), the luminance (brightness: Y), and the hue With respect to the YCrCb format that expresses a color with the information (color shade: CrCb), a color picker similar to that in the RGB format can be configured using the present invention.

  Further, for example, it is conceivable to arrange product information and the like three-dimensionally on a so-called net shopping product designation screen. In such a case, the square area of the Sherpinski carpet with a predetermined resolution is associated with the voxels (stored product information) constituting the voxel space in advance, or the correspondence rules as described above are used. For example, by designating any square area of the Sherpinski carpet, it is possible to easily access product information arranged three-dimensionally (even if it is hidden and not visible). Become. Similarly, for example, in the management software of a three-dimensional warehouse or a three-dimensional parking lot, it is conceivable to arrange the inventory information and the warehousing situation in a three-dimensional manner on the management screen. Even in such a case, the square area of the Sherpinsky carpet having a predetermined resolution is associated with the voxels (which store inventory information and warehousing information) constituting the voxel space in advance, or as described above. By using a correspondence rule, you can easily access information arranged in three dimensions (even if it is hidden and hidden) by specifying any square area on the Shelpinsky carpet. Is possible.

  Furthermore, by using the 3D coordinate setting function and the straight line / curve setting function as described above, it is possible to design a trajectory for object movement animation. For example, a 3D character follows a path. It will be useful when creating animations that progress in the future. Further, by using the above-described 3D coordinate setting function and curve setting function, a vector field along a curve set in a three-dimensional space (three-dimensional coordinate system) is calculated and a particle system is used. You can perform field design and visualization.

  FIG. 10 is a schematic configuration diagram of a computer 20A as a voxel modeling apparatus in which a voxel modeling program according to the present invention is installed. In the following description, the same reference numerals are assigned to the same elements as the elements described so far, and a duplicate description is omitted.

As shown in FIG. 10, when the voxel modeling program is started in the computer 20 </ b> A, a window 90 </ b> A is displayed on the display screen 31 of the display device 30. Window 90A includes a 2D coordinate designation area 92A and a 3D image display area 93A. In the 2D coordinate designation area 92A as a two-dimensional space, the N-th stage Shelpinsky carpet 100A is displayed, and when the user selects any square area of the Sherpinski carpet 100A, for example, the square The area appears to be filled. The 3D image display area 93A includes a 2D position (xy coordinates in pixel units) designated (selected) by the user on the Sherpinsky carpet 100A displayed in the 2D coordinate designation area 92A, that is, any square area. A 3D image 300 showing the three-dimensional shape set by the modeling unit 23A based on the voxels corresponding to is displayed. In the example of FIG. 10, the modeling unit 23 uses the above-described correspondence rule (table), and 2 ^N × 2 ^N × 2 of one voxel corresponding to the square area designated on the Sherpinski carpet 100. A position in a voxel space made up of ^N voxels is acquired, and the three-dimensional shape is set so as to cut out the cube by erasing the voxel at the acquired position.

  In this way, it is possible to associate the Shelpinsky carpet of resolution N (Nth stage) with the voxel space and specify the three-dimensional position in the three-dimensional space by specifying the two-dimensional position on the two-dimensional space. For example, voxel modeling that expresses a three-dimensional shape as a set of voxels can be easily executed. In addition, when a three-dimensional shape is modeled using a Shelpinsky carpet having a resolution N in this manner, voxel model data corresponding to a resolution smaller than the value N can be obtained. Then, according to the computer 20A in which the voxel modeling program is installed, by providing a voxel value to each voxel, unlike the polygon modeling, the density inside the shape as well as the surface of the three-dimensional shape. It is possible to model even internal data. The three-dimensional shape obtained by voxel modeling does not have a smooth surface. For example, see the Marching Cube method (Lorensen WE, Cline HE, "Marching Cubes: A High Resolution 3D Surface Construction Algorithm", etc.) ) Can be used to approximate a three-dimensional surface to a smooth one. In the example of FIG. 10, the three-dimensional shape is set by erasing the voxel corresponding to the square area designated on the Sherpinski carpet 100 from the voxel space. However, the present invention is not limited to this. . That is, the three-dimensional shape may be set so that voxels corresponding to the designated square area on the Sherpinski carpet 100 are stacked, that is, as a set of voxels corresponding to the designated square area.

  The embodiments of the present invention have been described above using the embodiments. However, the present invention is not limited to the above embodiments, and various modifications can be made without departing from the scope of the present invention. Needless to say.

  The present invention can be used in the information processing field that requires designation of a three-dimensional position in a three-dimensional space and three-dimensional shape expression.

1 is a schematic configuration diagram of a computer 20 as a three-dimensional position designation apparatus in which a three-dimensional position designation program according to an embodiment of the present invention is installed. 12 is an explanatory diagram illustrating an example of a window 90 displayed on the display screen 31 of the display device 30. FIG. It is a flowchart which shows an example of the 3D coordinate setting routine performed in the computer 20 of an Example. It is explanatory drawing for demonstrating the correspondence rule in an Example. It is explanatory drawing which shows an example of the table which matches 8 square area | regions and the 3D coordinate of 8 voxels which comprise the 1st stage Sherpinski carpet. It is explanatory drawing which shows the procedure which pinpoints the square area | region of the Nth step Sherpinski carpet corresponding to 2D coordinate (x, y). 8 ^N pieces of 2D coordinates from a voxel constituting the voxel space (x, y) a procedure for characterizing the voxels corresponding to an explanatory view schematically showing. It is a flowchart which shows an example of the coordinate transformation process in step S120 of FIG. It is a flowchart which shows an example of 3D drawing routine performed in the computer 20 of an Example. It is a schematic block diagram of computer 20A as a voxel modeling apparatus in which the voxel modeling program based on the application example of this invention was installed.

Explanation of symbols

  20, 20A computer, 21 input reception unit, 22 information storage unit, 23, 23A modeling unit, 24 display control unit, 30 display device, 31 display screen, 40 keyboard, 50 mouse, 90, 90A window, 92, 92A 2D coordinates Designated area, 93, 93A 3D image display area, 95 buttons, 100, 100A Sherpinsky carpet, 300 3D image.

Claims (8)

A three-dimensional position designation device for designating a three-dimensional position in a three-dimensional space,
Two-dimensional position specifying means for specifying a two-dimensional position in a two-dimensional space;
A two-dimensional position designated by the two-dimensional position designation means of the Nth stage Sherpinski carpet having an array of 8 ^N squares (where “N” is an integer equal to or greater than 1). Are associated with any one of 2 ^N × 2 ^N × 2 ^N voxels constituting a voxel space according to a predetermined correspondence rule, and the one region associated with the square region Computing means for obtaining a three-dimensional position in the three-dimensional space based on a position of the voxel in the voxel space;
A three-dimensional position specifying device. The three-dimensional position specifying device according to claim 1,
The correspondence rule stipulates the correspondence between the 8 square regions constituting the first Sherpinski carpet and the 2 × 2 × 2 voxels constituting one volume,
The computing means is the n-th square area corresponding to the designated two-dimensional position of the Sherpinsky carpet in the n-th stage (where “n” is an integer satisfying 1 ≦ n ≦ N). The designation in a voxel space composed of 2 ⁿ × 2 ⁿ × 2 ⁿ voxels based on the position in the square area corresponding to the designated two-dimensional position of the one-step Sherpinski carpet and the correspondence rule. Obtaining a position in the voxel corresponding to the specified two-dimensional position in a voxel space composed of 2 ^n-1 × 2 ^n-1 × 2 ^n-1 voxels of the voxel corresponding to the specified two-dimensional position; A three-dimensional position designation device that acquires a three-dimensional position in the three-dimensional space based on the acquired positions of n voxels. The three-dimensional position specifying device according to claim 1 or 2,
The conversion rule is to draw eight square areas of the first-stage Sherpinski carpet according to the order on the one-stroke path determined for them, with respect to 2 × 2 × 2 voxels. A three-dimensional position specifying device which is a rule assigned to follow a writing path. In the three-dimensional position designation device according to any one of claims 1 to 3 ,
Display means capable of displaying an image on the display screen;
Display control means for displaying an image based on the N-th stage Shelpinski carpet on the display screen and plotting the three-dimensional coordinates indicating the three-dimensional position acquired by the computing means on the display screen. When,
A three-dimensional position specifying device further comprising: The three-dimensional position specifying device according to claim 4 ,
The display control means plots the three-dimensional coordinates indicating the three-dimensional position acquired by the computing means on the display screen, and displays an image based on a voxel having a predetermined size around the three-dimensional position. Dimensional positioning device. A three-dimensional position designation program that causes a computer to function as a device for designating a three-dimensional position in a three-dimensional space,
A two-dimensional position specifying module for specifying a two-dimensional position specified in a two-dimensional space;
A square area corresponding to the specified two-dimensional position of the N-th stage Sherpinski carpet having an array of 8 ^N square areas (where “N” is an integer equal to or greater than 1) Corresponding to any one of 2 ^N × 2 ^N × 2 ^N voxels constituting the voxel space according to the correspondence rule, and at the position of the one voxel associated with the square region in the voxel space An arithmetic module that obtains a three-dimensional position in the three-dimensional space based on;
A three-dimensional position designation program comprising: A voxel modeling device capable of expressing a three-dimensional shape as a set of voxels,
Two-dimensional position specifying means for specifying a two-dimensional position in a two-dimensional space;
A two-dimensional position designated by the two-dimensional position designation means of the Nth stage Sherpinski carpet having an array of 8 ^N squares (where “N” is an integer equal to or greater than 1). Are associated with any one of 2 ^N × 2 ^N × 2 ^N voxels constituting a voxel space according to a predetermined correspondence rule, and the one region associated with the square region Position acquisition means for acquiring a position of the voxel in the voxel space;
Shape setting means for setting a three-dimensional shape based on voxels at positions acquired by the position acquisition means;
A voxel modeling device. A voxel modeling program for causing a computer to function as a device for expressing a three-dimensional shape as a set of voxels,
A two-dimensional position specifying module for specifying a two-dimensional position specified in a two-dimensional space;
A square area corresponding to the specified two-dimensional position of the N-th stage Sherpinski carpet having an array of 8 ^N square areas (where “N” is an integer equal to or greater than 1) Corresponding to any one of 2 ^N × 2 ^N × 2 ^N voxels constituting the voxel space according to the correspondence rule, and the position of the one voxel associated with the square region in the voxel space A position acquisition module to acquire, a shape setting module to set a three-dimensional shape based on the voxel of the acquired position,
Voxel modeling program provided.

Images